How to create a 3-D Cardioid shape in MatLab? (a cylinder with a cardioid base)

Currently, I am able to plot a 2-D cardioid in MatLab using this code:

% 2-Dimensional Cardioid
theta = linspace(0, 2*pi);
r = 1-(0.7*sin(theta));
plot(r.*cos(theta) *1.25, (r.*sin(theta) *1.25))

axis equal
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
xlim([-3.5 3.5]) 
ylim([-3.5 3.5])
zlim([-3.5 3.5])

However, I would like to plot a 3-D cardioid, such that there is the z-dimension included.

(At the moment, the cardioid is only in 2-D, as it solely includes the x-dimension and y-dimension)

Here is the idea I want to visualize in MatLab please:

(The idea is a 3D cylinder with a cardioid-shaped base)

Is anyone able to provide some advice or insight into how to create this please? Thank you for your help.

Answer 1

[DGM]

Here's one way.

% 2-Dimensional Cardioid
theta = linspace(0, 2*pi);
r = 1-(0.7*sin(theta));
x = r.*cos(theta)*1.25;
y = r.*sin(theta)*1.25;

% expand everything
zlevels = 10;
zrange = [-1 1];
X = repmat(x,[zlevels 1]);
Y = repmat(y,[zlevels 1]);
Z = linspace(zrange(1),zrange(2),zlevels);
Z = repmat(Z.',[1 numel(x)]);

% plot using surf()
hs = surf(X,Y,Z);
hs.FaceColor = [0.65 0.6 1];
hl = lightangle(gca,45,45);
material(hs,[0.5 1 1])
set(gca,'projection','perspective')
view([-46 38])
axis equal

xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
xlim([-2 2]) 
ylim([-2.5 1.5])
zlim([-2 2])

You'll probably want to play with the colormapping and lighting as you see fit.

[Charles]

Yes!! Thank you! You are a MatLab genius. This is so helpful, exactly the idea in my mind. Love this community.

[Charles]

Edit/Update: From what I see, you edited your original answer or code. In my opinion, the code you originally posted (before your edit) was a better version. Originally, you used the "surf" function without the new hs or hl, and the overall code was more concise.

[DGM]

I was just trying to approximate the figure setup that would have been used to create the sample image. All of the additional fluff (lighting, color, projection) can simply be omitted.

% 2-Dimensional Cardioid
theta = linspace(0, 2*pi);
r = 1-(0.7*sin(theta));
x = r.*cos(theta)*1.25;
y = r.*sin(theta)*1.25;

% expand everything
zlevels = 10;
zrange = [-1 1];
X = repmat(x,[zlevels 1]);
Y = repmat(y,[zlevels 1]);
Z = linspace(zrange(1),zrange(2),zlevels);
Z = repmat(Z.',[1 numel(x)]);

% plot using surf()
surf(X,Y,Z);
axis equal

xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
xlim([-2 2]) 
ylim([-2.5 1.5])
zlim([-2 2])

[Charles]

Awesome! Thank you, this is great!

Answer 2

[Dyuman Joshi]

Use the implicit equation of Cardiod as input to fimplicit3 and define x, y and z limits required -

% 2-Dimensional Cardioid
a = 1.25;

%Equation referenced from Wikipedia, not the same as used above
eqn = @(x,y,z) (x.^2+y.^2).^2 + 4.*a.*x.*(x.^2+y.^2) - 4.*a^2.*y.^2;

%The intervals defined are [xmin xmax ymin ymax zmin zmax]
fimplicit3(eqn, [-2*pi 2*pi -5 5 -2 2])
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')

[Charles]

Thanks! This is also a nice method. Thank you for the help!